How to find the Python equivalent operation for tools, settings & menu?
Edit Source

If you wanted to find out the python code for some of the user interface and panels you could right-click on parts of the UI (such as buttons or properties within the panel you wanted to know about) and choose 'Edit Source'.

For example, if I wanted to know about the render panel:



I could right-click on the 'Render' button and choose 'Edit Source':



A notification will then appear in the Info header at the top of the screen (in a default layout) informing you that a text file had been created for viewing in the text editor:



You can check this file and view the python code that makes up the panel:



In this example you can see information which might be useful such as: The panel class name which can be used to append new UI elements into existing parts of the UI (RENDER_PT_render), the operator names and categories (render.render for example) and general UI code for creating rows (row = layout.row(align=True)).

Autocomplete

Sometimes, if you are searching for the python equivalent of a property, it might be useful to use the autocomplete feature (CTRL+Space) of the 'Python Console' to explore the api.

Autocomplete will show you all the possible options branching off the current one. For example, using autocomplete on bpy.data.objects['Cube'] would result in showing me all the available python properties for that object:



Online API documentation

You can also browse the online 'Python API Reference' (that link always redirects to the latest version) which can be found via the help menu:



This documentation includes several pages serving as an introduction to the API as well as a full reference to all the python commands and properties available to use in blender. While this doesn't provide the python command to an exact tool/panel instantly, a simple generic search of "panel" using the search box would provide results relating to existing panels in blender and examples of how to create a new one.

Hotkey Preferences

If you wanted to find out the python name of a menu that appears when you press a hotkey, you can search for that hotkey in the preferences. For example, if I wanted to know the python name of the menu that appears when I press Ctrl+H in edit mode (the hook menu), I can search using the shortcut (when search type is 'key binding') in File> User Preferences> Input:



This provides several results, one of which is a 'Call Menu' item in the 'Mesh' category which reveals the name of the menu being called:



Here we can see the menu being called with that shortcut is VIEW3D_MT_hook, which you can then call in your own scripts.